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Investigation and Implementation of Parallelism Resources of Numerical algorithms

ACM TRANSACTIONS ON PARALLEL COMPUTING 2023年第2期10卷 1-64页

作者： Aleeva, Valentina Aleev, Rifkhat South Ural State Univ Natl Res Univ 76 Prospect Lenina Chelyabinsk 454080 Russia

This article is devoted to an approach to solving a problem of the efficiency of parallel computing. The theoretical basis of this approach is the concept of a q-determinant. Any numerical algorithm has a q-determinant. The q-determinant of the algorithm has clear structure and is convenient for implementation. The q-determinant consists of q-terms. Their number is equal to the number of output data items. Each q-term describes all possible ways to compute one of the output data items based on the input data. We also describe a software q-system for studying the parallelism resources of numerical algorithms. This system enables to compute and compare the parallelism resources of numerical algorithms. The application of the q-system is shown on the example of numerical algorithms with different structures of q-determinants. Furthermore, we suggest a method for designing of parallel programs for numerical algorithms. This method is based on a representation of a numerical algorithm in the form of a q-determinant. As a result, we can obtain the program using the parallelism resource of the algorithm completely. Such programs are called q-effective. The results of this research can be applied to increase the implementation efficiency of numerical algorithms, methods, as well as algorithmic problems on parallel computing systems.

关键词： q-term of algorithm q-determinant of algorithm representation of algorithm in form of q-determinant q-effective implementation of algorithm parallelism resource of algorithm software q-system q-effective program q-effective programming

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Improving Parallel Computing Efficiency

Improving Parallel Computing Efficiency

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Global Smart Industry Conference (GloSIC)

作者： Aleeva, Valentina N. South Ural State Univ Natl Res Univ Chelyabinsk Russia

ISBN: (纸本)9781728180755

In this paper some approach to solving a problem of the efficiency of parallel computing is considered on the base of the concept of a q-determinant. Any numerical algorithm has a q-determinant that is convenient for implementation. The content of every q-determinant are q-terms that number is equal to the number of output data items. On the base of the input data each of q-terms allows for the considering of all possible ways to compute one of the output data items. We also describe a software q-system for studying the parallelism resource of numerical algorithms. Furthermore, we suggest a method for designing of parallel programs for numerical algorithms. As a result, we can obtain the program with complete the parallelism resource of the algorithm. Such programs are called q-effective. We also suggest the technology of q-effective programming. On the base of this research we can increase the efficiency of implementation of numerical algorithms, methods, as well as algorithmic problems on parallel computing systems.

关键词： q-determinant of algorithm representation of algorithm in form of q-determinant q-effective implementation of algorithm parallelism resource of algorithm height of algorithm width of algorithm q-effective program

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High-Performance Computing Using Application of q-determinant of Numerical algorithms

High-Performance Computing Using Application of Q-determinan...

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Global Smart Industry Conference (GloSIC)

作者： Aleeva, Valentina N. Aleev, Rifkhat Zh. Natl Res Univ South Ural State Univ Chelyabinsk Russia

ISBN: (纸本)9781538673867

The conception of q-determinant is one of the approaches to parallelizing numerical algorithms. The basic notion of the conception is q-determinant of the algorithm. Here q is the set of operations used by the algorithm. The q-determinant consists of q-terms. Their number is equal to the number of output data. Each q-term describes all possible ways to calculate one of the output data based on the input data. Any numerical algorithm has a q-determinant and can be represented in the form of a q-determinant. This representation is a universal description of numerical algorithms. The representation algorithm in the form of q-determinant makes the numerical algorithm in terms of the structure and implementation clearer. Although q-determinant contains only machine-independent properties of the algorithm it can be used to implement algorithms on parallel computing systems. The paper describes the application of the q-determinant to determine the parallelism resource of numerical algorithms and to develop q-effective programs. A q-effective program uses the parallelism resource of algorithm completely. At the present time the available theoretical results have been tested for numerical algorithms with various structures of q-determinants. For example, they include multiplication algorithms for dense and sparse matrices, Gauss-Jordan, Jacobi, Gauss-Seidel methods for solving the systems of linear equations, the sweep method and the Fourier method for solving grid equations, and others. The results of the research can be used to increase the efficiency of implementing numerical algorithms on parallel computing systems.

关键词： q-determinant of algorithm algorithm representation as q-determinant q-effective implementation of algorithm q-effective program parallelism resource of algorithm parallel computing system parallel program

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Software q-system for the Research of the Resource of Numerical algorithms Parallelism 5th

Software Q-system for the Research of the Resource of Numeri...

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5th Russian Supercomputing Days Conference (RuSCDays)

作者： Aleeva, Valentina Bogatyreva, Ekaterina Skleznev, Artem Sokolov, Mikhail Shuppa, Artemii South Ural State Univ Natl Res Univ Chelyabinsk Russia

ISBN: (纸本)9783030365929;9783030365912

The paper describes software q-system for research of the resource of numerical algorithms parallelism. The theoretical basis of the q-system is the concept of q-determinant where q is the set of operations used by the algorithm. The q-determinant consists of q-terms. Their number is equal to the number of output data items. Each q-term describes all possible ways to calculate one of the output data items based on the input data. Any numerical algorithm has a q-determinant and can be represented in the form of a q-determinant. Such a representation is a universal description of numerical algorithms. It makes the algorithm transparent in terms of structure and implementation. The software q-system enables to calculate the parallelism resource of any numerical algorithm, and also to compare the parallelism resources of two algorithms that solve the same algorithmic problem. In the paper we show the application of the q-system on the example of numerical algorithms with different structures of q-determinants. Among them, we have the matrix multiplication algorithm, methods of Gauss-Jordan, Jacobi, Gauss-Seidel for solving systems of linear equations, and other algorithms. The paper continues the research begun in the previous papers of the authors. The results of the research can be used to increase the efficiency of implementing numerical algorithms on parallel computing systems.

关键词： q-term of algorithm q-determinant of algorithm Representation of the algorithm in the form of q-determinant q-effective implementation of algorithm Parallelism resource of algorithm Height of the algorithm Width of the algorithm Software q-system Parallel computing system Parallel program q-effective program

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